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Transcript
Optometric Care within the Public Health Community
© 2009 Old Post Publishing 1455 Hardscrabble Rd. Cadyville, NY 12918
EPIDEMIOLOGY
Robert D. Newcomb, OD, MPH, FAAO
Whoever wishes to investigate medicine properly, should proceed thus: in the first place to
consider the seasons of the year, and what effects each of them produces for they are not all
alike, but differ much from themselves in regard to their changes. Then the winds, the hot and the
cold, especially such as are common to all countries, and then such as are peculiar to each
locality.
from Airs, Waters, and Places
Hippocrates (460-370 B.C.)
Chapter Overview
Epidemiology (epi = upon, demos = population, ology = word, thought, the study of) is
the basic science of all public health activities. If diseases, disorders, and conditions
affecting the human body were randomly distributed within a given population, thenthere
would be no way for researchers to predict who might be affected by them at a later
point in time; and therefore, certainly no way to prevent them from occurring. So the
science of epidemiology helps us understand why some members of a population
develop a clinical finding while other members of that same population do not. And
having this type of information allows clinicians to prevent diseases, disorders and
conditions in addition to treating them earlier and more effectively.
This chapter will briefly discuss the scientific principles, terminology, and
applications of epidemiology. Examples from the medical, eye, and vision literature will
be employed to emphasize the relevance of this basic science to the daily practice of
optometry.
Objectives
On completion of this chapter, the reader should be able to
1. Calculate the Relative Risk that a given risk factor has on predicting a
morbidity (or mortality) rate.
2. Categorize patients by age, sex, race, socioeconomic status, medical
history, and other demographic variables and learn to use these
categories as predictors of various diseases, disorders, or conditions.
3. Identify high-risk sub-groups of people as a way to begin addressing
the causes of health disparities in large populations.
4. Design an epidemiological research project to identify pertinent risk
factors that predict which members of a population are “at risk” for
developing a specific disease, disorder, or condition.
Epidemiology Robert Newcomb
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Optometric Care within the Public Health Community
© 2009 Old Post Publishing 1455 Hardscrabble Rd. Cadyville, NY 12918
Demography: The Study of Populations
While clinicians must think in terms of individual patients who are seated in their
examination chairs, epidemiologists prefer to think of those same patients as members
of a much larger group of comparable people. Austin and Werner 1 have defined the
word “Epidemiology” as “…the study of how and why diseases and other conditions are
distributed within the population the way they are.” Populations can be defined as any
small, medium, or large group of people. A population could be defined as all the
students in one classroom, all the people working in an office building, all the citizens of
a city or state, or even all of the people living on planet earth! Data from these studies
would provide examples of descriptive epidemiology. But describing these populations
of people solely on the basis of their common locations would be counterproductive
unless one could analyze them in terms of other risk factors for certain diseases. So the
next logical step of epidemiology research would be analytical. Only then would
researchers be able to identify both inherent (ie, age, sex, race) and acquired (do you
smoke? are you obese? have you been exposed to hazardous materials?) risk factors
which may predispose a sub-set of that population to excessive disease rates.
For example, there are about 305 million people living in the United States; and
about 6 billion people living on planet earth. If diseases were distributed randomly in
these two large populations, everyone would need the same amount of health care at
predictable stages in their lives. But, as shown later in this chapter, disease rates are
not the same in the US as they are in the rest of the world; and they are not even the
same between groups within the US borders.
Incidence and Prevalence
Incidence rates are measures of only the new cases of a disease that occur during a
given time period such as months, years, or decades within a population susceptible to
the disease of interest. Mortality, for example, is the incidence of deaths per thousand
per year in a defined population. Prevalence rates are measures of all cases (both new
and old) of a disease that are present (or prevail) at one point in time. Prevalence is not
actually a rate but a proportion and is usually reported as a percentage. For example, in
2002, a meta-analysis by the National Eye Institute and Prevent Blindness America
reported the prevalence of glaucoma was 1.9% of the total U.S. population age 40 and
older.2
In acute diseases, such as conjunctivitis (“pink eye”) in an elementary school,
incidence measures are more useful because it is a limited but highly-contagious
condition. Such conditions may be seasonal, so comparison of a current incidence rate
with historical data may establish an epidemic (loosely defined as more cases of a
disease than would normally be expected). But in chronic diseases that are not
contagious, such as cancer or glaucoma, prevalence measures are more useful
because public health officials can monitor whether or not these conditions are
increasing, decreasing, or remaining constant in a community, state, or nation over
time, and can then begin to research underlying causes of the variation in data.
Epidemiology Robert Newcomb
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Optometric Care within the Public Health Community
© 2009 Old Post Publishing 1455 Hardscrabble Rd. Cadyville, NY 12918
Descriptive Epidemiology
At its most basic level, the science of epidemiology is used to simply count the
number of people who have a certain disease, disorder, or condition. The Who? What?
Where? and When? –type questions can be answered by descriptive epidemiology
studies. The result of this counting is usually expressed as a fraction, where the number
of people who are affected is shown in the numerator, and the denominator is the size
of the population from which they came. This fraction can then be converted to a
decimal or percentage, so different populations can be easily compared with each other.
Consider the descriptive epidemiology data in Tables 1-4 from the World Health
Organization.3
Table 1. Top Ten Causes of Death in the World
Deaths in
millions
% of
deaths
Coronary heart disease
7.20
12.2
Stroke and other cerebrovascular diseases
5.71
9.7
Lower respiratory infections
4.18
7.1
Perinatal conditions
3.18
5.4
Chronic obstructive pulmonary disease
3.02
5.1
Diarrheal diseases
2.16
3.7
HIV/AIDS
2.04
3.5
Tuberculosis
1.46
2.5
Trachea, bronchus, lung cancers
1.32
2.3
Road traffic accidents
1.27
2.2
Source: World Health Organization, September, 2008
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Optometric Care within the Public Health Community
© 2009 Old Post Publishing 1455 Hardscrabble Rd. Cadyville, NY 12918
Table 2. Top Ten Causes of Death in low-income countries
Deaths in
millions
% of
deaths
Lower respiratory infections
2.94
11.2
Coronary heart disease
2.47
9.4
Perinatal conditions
2.40
9.1
Diarrheal diseases
1.81
6.9
HIV/AIDS
1.51
5.7
Stroke and other cerebrovascular diseases
1.48
5.6
Chronic obstructive pulmonary disease
0.94
3.6
Tuberculosis
0.91
3.5
Malaria
0.86
3.3
Road traffic accidents
0.48
1.9
Deaths in
millions
% of
deaths
Stroke and other cerebrovascular diseases
3.47
14.2
Coronary heart disease
3.40
13.9
Chronic obstructive pulmonary disease
1.80
7.4
Lower respiratory infection
0.92
3.8
Perinatal conditions
0.75
3.1
Trachea, bronchus, lung cancers
0.69
2.9
Road traffic accidents
0.67
2.8
Hypertensive heart disease
0.62
2.5
Source: World Health organization, September, 2008
Table 3. Top Ten Causes of death in middle-income countries
Epidemiology Robert Newcomb
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Optometric Care within the Public Health Community
© 2009 Old Post Publishing 1455 Hardscrabble Rd. Cadyville, NY 12918
Stomach cancer
0.55
2.2
Tuberculosis
0.54
2.2
Deaths in
Millions
% of
deaths
Coronary heart disease
1.33
16.3
Stroke and other cerebrovascular diseases
0.76
9.3
Trachea, bronchus, lung cancers
0.48
5.9
Lower respiratory infections
0.31
3.8
Chronic obstructive pulmonary disease
0.29
3.5
Alzheimer and other dementias
0.28
3.4
Colon and rectum cancers
0.27
3.3
Diabetes mellitus
0.22
2.8
Breast cancer
0.16
2.0
Stomach cancer
0.14
1.8
Source: World Health organization, September, 2008
Table 4. Top Ten causes of death in high-income countries
Source: World Health organization, September, 2008
They indicate different diseases - and different frequencies of the same diseases –
occur depending upon where people live. Why is this? Is it because of Genetics?
Economics? the Environment? Varying levels of Health Education and/or Health
Literacy? Access to Health Care? Lack of basic Public Health Infrastructures such as
surveillance systems, prevention strategies, quality assurance measures, and/or
excessively low provider/population ratios? A descriptive epidemiology study cannot
answer the Why? –type question; but a well-designed analytical epidemiologic research
project (see below) in each country could begin to address all of these possible risk
factors for its citizens.
Another example of descriptive epidemiology is shown in Figure 1, which shows
how legal blindness increases with age among Americans who are 40 years old and
older in four different race and ethnic groups.
Epidemiology Robert Newcomb
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Optometric Care within the Public Health Community
© 2009 Old Post Publishing 1455 Hardscrabble Rd. Cadyville, NY 12918
Multi-factorial
diseases…likely
have more than
one risk factor
contributing to
the onset of the
disease.
The first
observation from these data would be that the frequency of blindness increases
dramatically as people age, regardless of their race or ethnicity. This fact can be
explained by knowing that the number of cataract, age-related macular
degeneration, glaucoma, and diabetic retinopathy cases also increase as people
age. But a more detailed examination of the data show that black patients in the
75-79 year-old age category have 3 times the amount of blindness as similarlyaged white and Hispanic patients. And Hispanic patients in the 85+ age category
have only one-third the amount of blindness as similarly-age white and black
patients. What variables (factors) might explain these marked differences in
blindness? Again, a descriptive epidemiology study such as this cannot answer
the Why? –type question; but a well-designed analytical epidemiologic research
project can.
Analytical Epidemiology
To better understand and test theories for why certain diseases are distributed
differently in different populations, epidemiologists must perform analytical studies.
These studies attempt to explain the differences based upon certain variables, or risk
factors, that are present in some people but not present in others. Analytical
Epidemiology Robert Newcomb
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© 2009 Old Post Publishing 1455 Hardscrabble Rd. Cadyville, NY 12918
epidemiologists then attempt to explain, or attribute, these differences by using
mathematical concepts such as rates, ratios, and risk factors. Often, these analytical
studies establish a relationship, also known as an association, between a specific risk
factor and a disease; these associations may be weak or strong, and even direct or
inverse The ultimate goal for analytical epidemiologists is to discover a cause-and-effect
association between a risk factor and a disease. This direct cause-and-effect
association is more commonly found in infectious diseases, where the cause is a
specific microorganism such as the tubercule bacillus in tuberculosis. But in chronic
diseases such as heart disease, hypertension, and diabetes, there is rarely a single
cause that can be identified. So these conditions may be termed multi-factorial
diseases, which means they likely have more than one risk factor contributing to the
onset of the disease.
A very good recent example of analytical epidemiology in optometry was
published by Charlotte Joslin, OD, et al, in 2006 entitled Epidemiological Characteristics
of a Chicago-area Acanthamoeba Keratitis Outbreak4. In her study of 40 patients
diagnosed with Acanthamoeba keratitis (AK) over a thirty-month time period, she found
a statistically and clinically significant increase in the incidence of AK cases around
Chicago; and hypothesized that the U.S. Environmental Protection Agency’s 1998
regulations that reduced the allowable amount of carcinogenic disinfection by-products
in public water treatment systems may be a likely explanation for her findings.
Experimental Epidemiology
Since any given patient can have any specific diagnosis at any time (“it ain’t rare if it’s
in your chair”), the science of epidemiology requires researchers to study and compare
two similar groups of people which, ideally, differ only in having one isolated risk factor.
This is known as experimental epidemiology. Both descriptive and analytical
epidemiology studies are known as observational, or “natural experience” studies,
where the investigator observes but does not manipulate either disease frequencies or
risk factor exposures in the population. In contrast, experimental epidemiology studies
are “investigator controlled,” so that research studies called Randomized Clinical Trials
(RCT’s) can be designed to statistically measure the effect of a given risk factor on the
presence or absence of a certain disease.
An example of a recent and well-designed Randomized Clinical Trial in
optometry is the Convergence Insufficiency Treatment Trial (CITT).5 This National Eye
Institute (NEI) sponsored multi-center clinical trial enrolled 221 children, aged 9 to 17,
who had symptomatic convergence insufficiencies. These children were then randomlyassigned by the investigators to one of four treatment groups. And after 12 weeks of
treatment, the office-based vergence/accommodation therapy with home reinforcement
group had statistically-significant improvements in their symptom survey scores, and
also increases in their near points of convergence and increased positive fusional
vergence ranges compared to the other three treatment groups.
This study achieved one of the ultimate goals that all experimental
epidemiologists have: to present such compelling research data that it establishes a
Epidemiology Robert Newcomb
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Optometric Care within the Public Health Community
© 2009 Old Post Publishing 1455 Hardscrabble Rd. Cadyville, NY 12918
new standard of care for treating patients. Dr. Paul A. Sieving, Director of the National
Eye Institute, complimented the CITT investigators by stating “The CITT will provide eye
care professionals with the research they need to assist children with this condition.”6
Experimental epidemiology can be either prospective (where two groups of
subjects, one with the risk factor and the other without, are followed over time to see
who eventually get a disease) or retrospective (where the histories of affected and
unaffected subjects are studied to determine which risk factors may or may not have
been responsible for a disease which occurred at a later time. After collecting the
pertinent data, comparisons can then be made to determine which one of the two
groups has developed more “disease” (or, in the case of the CITT study, which group
has better clinical outcomes from different therapeutic interventions).
The Natural History of Disease
To appropriately apply scientific epidemiological principles and methods to the everyday
practice of optometry, it is important to understand a concept known as the Natural
History of Disease. As stated previously in the chapter, if diseases, disorders, and
conditions affecting the human body were randomly distributed within a given
population, then there would be no way for
researchers to predict who might be affected by
…a good clinician’s knowledge
them at a later point in time.
of the natural history of a
Weiss7 and many others have stated that,
disease is as important as his or
with respect to disease prevention and control,
her understanding its
a good clinician’s knowledge of the natural
history of a disease is as important as his or her
pathophysiological cause.
understanding its pathophysiological cause.
Consider the following timeline for a chronic disease like diabetes:
→
Pre-natal
Treatment
(genetic)
Factors
→
→
Birth
Outcomes
Factors
→
→
Risk
Onset
→
Pathological
→
Clinical
Symptoms
→
Clinical
→
Diagnosis
Signs
In this construct, if a patient has a mother or father with diabetes, that patient inherits an
increased risk for developing the disease later in life from prenatal, or genetic, factors.
Sometime after birth, that same patient may be exposed to risk factors such as obesity,
sedentary lifestyle, hypertension, hypercholesterolemia, cigarette smoking, etc, which
may lead to cellular changes within the body (pathological onset) which then lead to
clinical symptoms (ie, polydipsia, polyphagia, polyuria) followed by clinical signs such as
an abnormal glucose tolerance test. After a diagnosis of diabetes is confirmed, the
patient’s physician will develop a treatment plan and monitor the patient for clinical
outcomes such good or poor glucose control and the presence of any complications
such as diabetic retinopathy.
Epidemiology Robert Newcomb
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Optometric Care within the Public Health Community
© 2009 Old Post Publishing 1455 Hardscrabble Rd. Cadyville, NY 12918
So when does the patient’s optometrist begin intervention to improve visual
acuity and prevent blindness? Ideally, it should be early in the natural history of the
disease and not after hemorrhages and exudates are observed in the late stages of the
disease. If an optometrist can examine a patient in the susceptible “risk factors” stage of
this terrible disease and provide health education to interrupt its natural progression on
to the pathological onset stage, blindness from diabetic retinopathy can be eliminated
because the precedent diabetic disease will have been eliminated!
Comparing Two Groups
The world-famous ophthalmic epidemiologist, Dr. Alfred Sommer, once said
“Epidemiology has two overriding characteristics: a preference for rates rather
than absolute numbers, and a peculiarly thoughtful approach to studies amounting to
applied common sense.8”
Comparisons between two groups can actually be made by using either Rates (a
fraction in which those affected are divided by everyone in a specified population)
during a specified period of time or Ratios (a fraction in which those affected are divided
by those not-affected in a specified population). Fractions describing diseases or
conditions are called morbidity data, whereas fractions describing death are called
mortality data. And when using rates or ratios to compare two groups of people, the
quintessential research tool is a 2x2 contingency table, as shown below:
Case
Control
Total
Factor
A
B
A+B
No Factor
C
D
C+D
Total
A+C
B+D
A+B+C+D
Relative Risk (RR) is defined as the risk of a disease (also known as a
“case”) occurring in the presence of a certain factor as compared to its
occurrence in the absence of that same factor. Mathematically, it can be
calculated as follows:
RR
=
prevalence of a case occurring in a population exposed to the factor
prevalence of a case occurring in a population not exposed to the factor
Or, using data from the 2x2 contingency table above,
RR
= A/ A+B
C/C+D
And the Ratio of people affected with the “case” compared with those unaffected
would be
Epidemiology Robert Newcomb
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Optometric Care within the Public Health Community
© 2009 Old Post Publishing 1455 Hardscrabble Rd. Cadyville, NY 12918
Ratio = A+C
B+D
To demonstrate how these concepts can be useful in an optometric practice, consider
the following scenario:
An optometrist has noticed a lot of “red eye” patients in her practice recently, and
wonders if they are related to wearing a new brand of soft contact lenses (SCLs). She
reviews her records for the past six months and discovers 20 of 50 patients fit with the
same new brand of SCLs have developed red eyes. Her records of 30 other
patients in comparable age, sex, and racial categories were also reviewed for
comparison, and she found 15 of those patients had also developed red eyes.
So 20 cases of red eyes developed out of 50 patients exposed to the new SCL and 15
cases out of 30 non exposed controls also developed red eyes. What is the Relative
Risk of getting red eyes if one wears the new brand of SCLs? And what is the Ratio of
getting red eyes compared to not getting red eyes in the two patient sub-populations?
Step 1: Construct a 2x2 Contingency Table, as follows:
Wore SCL’s
Developed red eyes
Did not develop red eyes
Total
20
30
50
Did not wear
SCL’s
15
15
30
Total
35
45
80
Step 2: Calculate Relative Risk (RR), as follows
RR = ______Rate of red eyes in a population wearing SCLs_______
Rate of red eyes in a comparable population not wearing SCL’s
RR = 20/(20+30) = 0.4
15/(15+15)
0.5
= 0.80
Step 2 Interpretation:
If RR is greater than 1.00, then the isolated factor increases the risk;
If RR is less than 1.00, then the isolated factor does not increase the risk (and
may even be protective!).
Epidemiology Robert Newcomb
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Optometric Care within the Public Health Community
© 2009 Old Post Publishing 1455 Hardscrabble Rd. Cadyville, NY 12918
If RR equals 1.00, then the isolated factor has no contribution to either getting or
not getting the disorder; the isolated factor is therefore an independent variable.
In this example, since the RR is calculated to be less than 1.00, wearing SCLs
does not increase the risk (also known as the chance or probability) of having red eyes;
and the underlying cause of the red eyes has not yet been definitively determined.
Step 3: In this small clinical study, what is the Ratio of red eye patients
among SCL wearers? What is the Ratio of red eye patients among non-SCL
wearers?
Ratio =
(in SCL)
__
Ratio
=
(in non-SCL)
Ratio
=
(in entire study)
All Affected
=
All Non-affected
__All Affected__ =
All Non-Affected
All Affected
=
All-Non-Affected
20
50
15
30
35
45
= 0.4
= 0.5
= 0.78
Step 3 Interpretation:
In this small study, 40% of SCL wearers developed red eyes while 50% of non
SCL wearers developed red eyes.
Odds Ratio (OR)
Another useful concept in epidemiology research is Odds Ratio (OR), which is
used when researchers want to compare the chance of an event happening in
two different groups of people (ie, cases and controls). 9 Statistically, the odds of
an event occurring is the probability of the event [p/(1-p)] divided by the
probability of the same event not occurring [q/(1-q)] or
OR = p/(1-p)
q/(1-q)
where p is the probability for the first group and q is the probability of the second
group.
Like RR, an odds ratio of 1.00 indicates that the event being studied is
equally likely in both cases and controls. But unlike Relative Risk (RR), which is
expressed as a decimal or percentage, the Odds Ratio (OR) is actually
Epidemiology Robert Newcomb
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Optometric Care within the Public Health Community
© 2009 Old Post Publishing 1455 Hardscrabble Rd. Cadyville, NY 12918
expressed as a ratio. Using data from the table above, p = A/(A+C) and q =
D/(B+D), so
OR = Odds of exposure in cases
Odds of exposure in controls
OR
=
___A/(A+C)___
__1 – [A/(A+C)]_____
B/(B+D)
1 – [B/(B+D)]
=
__0.4__
____ 0.6_____ = 0.67
_0.5__
1.0
0.5
OR = 0.67
A popular short cut formula is OR = (A*D)/(B*C) = (20)*(15)/(15)*(30) = 0.67
In this example, since the OR is less than 1.00,
the interpretation is that patients wearing SCL
are actually less likely to have red eyes than a
comparable group of non-SCL wearers. RR and
OR values are rarely equal to each other; but
in large, well-designed research studies of uncommon
events, the values of RR and OR may be almost
the same.
…in large, well-designed
research studies of uncommon
events, the values of RR and OR
may be almost the same.
Summary thoughts
In his book entitled The Ghost Map, author Steven Johnson describes the terrible
cholera epidemic in London during 1850’s. At the time, most people thought
cholera was spread person-to-person through contaminated air. But John Snow,
who was a respected anesthesiologist in London, observed that the
gastrointestinal tract – and not the lung - was the first organ affected in cholera
patients. Because of this astute clinical observation, he hypothesized that the
mysterious agent causing the cholera epidemic must be contained in food and/or
water, not the air. And when plotted the locations of death from cholera as
recorded in the meticulous vital statistics that his medical colleague, William Farr,
recorded in his Weekly Returns (a forerunner of the U.S. Centers for Disease
Control and Preventions’s WMMR: Weekly Morbidity and Mortality Report), Snow
concluded the “risk factor” for cholera was the water from the Broad Street pump.
When Snow showed his analytical epidemiologic data to the local authorities,
they removed the Broad Street pump handle and the cholera epidemic was over.
This story is significant in the history of epidemiology, because the noted German
microbiologist, Robert Koch, would not be able to identify the true causative
agent of cholera (which is the bacterium Vibrio cholera) for another thirty years.
Epidemiology Robert Newcomb
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Optometric Care within the Public Health Community
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Johnson brings this historic and premiere epidemiological success story to
bear on the major public health problems of the 21 st century by stating
The influence of the Broad Street maps extends beyond the realm of
disease. The Web is teeming with new forms of amateur cartography,
thanks to services like Google Earth and Yahoo! Maps. Where Snow
inscribed the location of pumps and cholera fatalities over the street grid,
today’s mapmakers record a different kind of data: good public schools,
Chinese takeout places, playgrounds, gay-friendly bars, open
houses….Anyone can create a map that shows you where streets
intersect and where hotels are….The maps now appearing are of a
different breed altogether: maps of local knowledge created by actual
locals.…10
Using sound, time-honored epidemiological principles, and having accurate,
contemporary data readily available now via the internet, allows today’s
epidemiologists an unparalleled opportunity to study the distribution and
determinants of health problems in populations at risk. And with this knowledge
will come better strategies to reduce the morbidity and mortality rates for a widevariety of diseases throughout the world.
References
1. Austin, DF and Werner, SB: Epidemiology for the health sciences. Charles C
Thomas, Springfield, IL, 1974, p. 4.
2. National Eye Institute and Prevent Blindness America. Vision problems in the
U.S: Prevalence of adult vision impairment and age-related eye disease in
America. Bethesda, MD, 2002. Available from: www.usvisionproblems.org
3. The 10 Leading Causes of Death by Broad Income Group, 2004. World
Health Organization, Geneva, Switzerland, Fact Sheet No 310/November,
2008. Available from:
http://www.who.int/mediacentre/factsheets/fs310_2008.pdf
4. Joslin, CE, Tu, EY, McMahon, TT, et al: Epidemiological characteristics of a
Chicago-area Acanthamoeba keratitis outbreak. Am J Ophthal, 142(2): 212217, 2006.
5. Convergence Insufficiency Treatment Trial Study Group. Randomized clinical
trial trial of treatments for symptomatic convergence insufficiency in children.
Arch Ophthal, 126(10): 1336-1349, 2008.
Epidemiology Robert Newcomb
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Optometric Care within the Public Health Community
© 2009 Old Post Publishing 1455 Hardscrabble Rd. Cadyville, NY 12918
6. NEI Press Release, Monday, October 13, 2008: More Effective Treatment
Identified for Common Childhood Vision Disorder. National Eye Institute,
National Institutes of Health, Bethesda, MD. Available from:
http://www.nei.nih.gov/news/pressreleases/101308.asp
7. Weiss, NS: Clinical epidemiology: the study of the outcome of illness, third
ed. Oxford Univ press, New York, 2006, pp. 143-156.
8. J Sommer, A: Epidemiology and statistics for the ophthalmologist. Oxford
University Press, New York, 1980, p. 3.
9. Marshall, EC: Research methodologies and statistics. Chapter 5 in Public
health and Community optometry, second edition, by RD Newcomb and EC
Marshall. Butterworths, Boston, 1990, pp. 52-53.
10. Johnson, S: The Ghost Map: the story of London’s most terrifying epidemicand how it changed science, cities, and the modern world. Riverhead books,
New York, 2006, pp 219-220.
Epidemiology Robert Newcomb
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